Certainly! Let's address each part of the question step-by-step.
(a) Calculating the Circumference of the Circle:
The circumference of a circle is given by the formula:
[tex]\[ \text{Circumference} = \pi \times \text{Diameter} \][/tex]
Given that the diameter of the circle is 6 feet, we can substitute this value into the formula:
[tex]\[ \text{Circumference} = \pi \times 6 \][/tex]
Using the value of [tex]\(\pi \approx 3.14159\)[/tex]:
[tex]\[ \text{Circumference} \approx 3.14159 \times 6 \][/tex]
[tex]\[ \text{Circumference} \approx 18.84956 \][/tex]
Therefore, the circumference of the circle is approximately [tex]\(18.85\)[/tex] feet.
(b) Calculating the Area of the Circle:
To find the area of the circle, we first need to determine the radius. The radius is half of the diameter. Given that the diameter is 6 feet:
[tex]\[ \text{Radius} = \frac{\text{Diameter}}{2} \][/tex]
[tex]\[ \text{Radius} = \frac{6}{2} \][/tex]
[tex]\[ \text{Radius} = 3 \text{ feet} \][/tex]
Now, we use the formula for the area of a circle:
[tex]\[ \text{Area} = \pi \times \text{Radius}^2 \][/tex]
Substituting the radius:
[tex]\[ \text{Area} = \pi \times 3^2 \][/tex]
[tex]\[ \text{Area} = \pi \times 9 \][/tex]
Using the value of [tex]\(\pi \approx 3.14159\)[/tex]:
[tex]\[ \text{Area} \approx 3.14159 \times 9 \][/tex]
[tex]\[ \text{Area} \approx 28.27433 \][/tex]
Therefore, the area of the circle is approximately [tex]\(28.27\)[/tex] square feet.
To summarize:
- The circumference of the circle is approximately [tex]\(18.85\)[/tex] feet.
- The area of the circle is approximately [tex]\(28.27\)[/tex] square feet.
